Can I bevel this shape cleanly?
Go into Edit Mode, select your whole mesh, and go to Face &gt; Tris to Quads. This merges adjacent triangular faces into quads, which the Bevel modifier (and pretty much anything else) works best with.
Try beveling again and it should work better. If you want to convert back to tris again after beveling, just go to Face &gt; Triangulate Faces.